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Some Schrödinger Operators with Power-Decaying Potentials and Pure Point Spectrum

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Abstract:

We construct (deterministic) potentials such that the Schrödinger equation on has dense pure point spectrum in for almost all boundary conditions at . As a by-product, we also obtain power-decaying potentials for which the spectrum is purely singular continuous on for all boundary conditions.

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  1. Universitä:t Osnabrück, Fachbereich Mathematik/Informatik, D-49069 Osnabrück, Germany.¶E-mail: cremling@mathematik.uni-osnabrueck.de, , , , , , DE

    Christian Remling

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  1. Christian Remling
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Received: 8 November 1996 / Accepted: 8 January 1997

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Remling, C. Some Schrödinger Operators with Power-Decaying Potentials and Pure Point Spectrum . Comm Math Phys 186, 481–493 (1997). https://doi.org/10.1007/s002200050117

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  • DOI: https://doi.org/10.1007/s002200050117

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